<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">ellibs</journal-id><journal-title-group><journal-title xml:lang="ru">Электронные библиотеки</journal-title><trans-title-group xml:lang="en"><trans-title>Russian Digital Libraries Journal</trans-title></trans-title-group></journal-title-group><issn pub-type="epub">1562-5419</issn><publisher><publisher-name>Казанский (Приволжский) федеральный университет</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26907/1562-5419-2021-24-3-505-530</article-id><article-id custom-type="elpub" pub-id-type="custom">ellibs-284</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>Системы образовательных проекций, уровней  и пререквизитов математической онтологии OntoMathEdu</article-title><trans-title-group xml:lang="en"><trans-title>Educational Projection Systems, Levels And Prerequisites  Of Mathematical Ontology OntoMathEdu</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Фалилеева</surname><given-names>М. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Falileeva</surname><given-names>M.</given-names></name></name-alternatives><email xlink:type="simple">mmwwff@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кириллович</surname><given-names>А. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Kirillovich</surname><given-names>A.</given-names></name></name-alternatives><email xlink:type="simple">alik.kirillovich@gmail.com</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Hевзорова</surname><given-names>О. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Nevzorova</surname><given-names>O.</given-names></name></name-alternatives><email xlink:type="simple">onevzoro@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Шакирова</surname><given-names>Л. Р.</given-names></name><name name-style="western" xml:lang="en"><surname>Shakirova</surname><given-names>L.</given-names></name></name-alternatives><email xlink:type="simple">liliana008@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Липачёв</surname><given-names>Е. К.</given-names></name><name name-style="western" xml:lang="en"><surname>Lipachev</surname><given-names>E.</given-names></name></name-alternatives><email xlink:type="simple">elipachev@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Дюпина</surname><given-names>А. Э.</given-names></name><name name-style="western" xml:lang="en"><surname>Dyupina</surname><given-names>A.</given-names></name></name-alternatives><email xlink:type="simple">anastasiya.dupina@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Казанский (Приволжский) Федеральный университет</institution></aff><aff xml:lang="en"><institution>Kazan (Volga region) Federal University</institution></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Казанский филиал Межведомственного суперкомпьютерного центра Российской академии наук</institution></aff><aff xml:lang="en"><institution>Joint Supercomputer Center of the Russian Academy of Sciences</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2021</year></pub-date><pub-date pub-type="epub"><day>28</day><month>06</month><year>2021</year></pub-date><volume>24</volume><issue>3</issue><fpage>505</fpage><lpage>530</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Фалилеева М.В., Кириллович А.В., Hевзорова О.А., Шакирова Л.Р., Липачёв Е.К., Дюпина А.Э., 2021</copyright-statement><copyright-year>2021</copyright-year><copyright-holder xml:lang="ru">Фалилеева М.В., Кириллович А.В., Hевзорова О.А., Шакирова Л.Р., Липачёв Е.К., Дюпина А.Э.</copyright-holder><copyright-holder xml:lang="en">Falileeva M., Kirillovich A., Nevzorova O., Shakirova L., Lipachev E., Dyupina A.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://ellibs.elpub.ru/jour/article/view/284">https://ellibs.elpub.ru/jour/article/view/284</self-uri><abstract><p>Представлены разработанные образовательные проекции, уровни и пререквизиты математической образовательной полилингвальной онтологии OntoMathEdu. Образовательная проекция рассматривается как формализация определенной системы предметной подготовки по математике. Она представляет себой подмножество концептов онтологии OntoMathEdu, которые структурированы на данном этапе развития онтологии с помощью двух дидактических отношений — образовательный уровень и пререквизит.
&#13;

Образовательные уровни выделены на основе стандартов обучения соответствующей системы образования, отношение пререквизит определяется последовательностью изучаемых понятий в той или иной системе образования.  
&#13;

В онтологии OntoMathEdu определены две проекции, представляющие образовательные системы России и Великобритании. Алгоритм построения онтологии через связывание различных проекций позволяет в дальнейшем пополнять ее новыми образовательными проекциями, которые можно использовать в системе полилингвального обучения математике.
</p></abstract><trans-abstract xml:lang="en"><p>The developed educational projections, levels and prerequisites of the mathematical educational multilingual ontology OntoMathEdu are presented. Educational projection is viewed as the formalization of a certain system of subject training in mathematics. It is a subset of OntoMathEdu ontology concepts, which are structured at this stage of ontology development using two didactic relationships – educational level and prerequisites.
&#13;

Educational levels are allocated on the basis of the teaching standards of the corresponding education system, the relation of prerequisites is determined by the sequence of the studied concepts in a particular education system.
&#13;

The OntoMathEdu ontology defines two projections representing the educational systems of Russia and Great Britain. The algorithm for constructing an ontology through linking various projections allows it to be further replenished with new educational projections, which can later be used in the system of multilingual teaching of mathematics.
</p></trans-abstract><kwd-group xml:lang="ru"><kwd>онтология</kwd><kwd>математическое образование</kwd><kwd>планиметрия</kwd><kwd>образовательная проекция</kwd><kwd>образовательный уровень</kwd><kwd>пререквизит</kwd></kwd-group><kwd-group xml:lang="en"><kwd>OntoMathEdu</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Taibi D., Fulantelli G., Dietze S., Fetahu B. Educational Linked Data on the Web – Exploring and Analysing the Scope and Coverage // In: Mouromtsev D. and D’Aquin M. (Eds.) Open Data for Education: Linked, Shared, and Reusable Data for Teaching and Learning. Lecture Notes in Computer Science. Springer, Cham. 2016. V. 9500. P. 16–37. https://doi.org/10.1007/978-3-319-30493-9_2.</mixed-citation><mixed-citation xml:lang="en">Taibi D., Fulantelli G., Dietze S., Fetahu B. Educational Linked Data on the Web – Exploring and Analysing the Scope and Coverage // In: Mouromtsev D. and D’Aquin M. (Eds.) Open Data for Education: Linked, Shared, and Reusable Data for Teaching and Learning. Lecture Notes in Computer Science. Springer, Cham. 2016. V. 9500. P. 16–37. https://doi.org/10.1007/978-3-319-30493-9_2.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Nahhas S., Bamasag O., Khemakhem M., Bajnaid N. Added Values of Linked Data in Education: A Survey and Roadmap // Computers. 2018. V. 7, No. 3. https://doi.org/10.3390/computers7030045.</mixed-citation><mixed-citation xml:lang="en">Nahhas S., Bamasag O., Khemakhem M., Bajnaid N. Added Values of Linked Data in Education: A Survey and Roadmap // Computers. 2018. V. 7, No. 3. https://doi.org/10.3390/computers7030045.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Lange Ch. Ontologies and languages for representing mathematical knowledge on the Semantic Web // Semantic Web. 2013. V. 4, No. 2. P. 119–158. URL: https://doi.org/10.3233/SW-2012-0059.</mixed-citation><mixed-citation xml:lang="en">Lange Ch. Ontologies and languages for representing mathematical knowledge on the Semantic Web // Semantic Web. 2013. V. 4, No. 2. P. 119–158. URL: https://doi.org/10.3233/SW-2012-0059.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Kohlhase M. A Data Model and Encoding for a Semantic, Multilingual Terminology of Mathematics // In: Watt S.M., et al. (Eds.) Proceedings of the International Conference on Intelligent Computer Mathematics (CICM 2014). Lecture Notes in Computer Science. . Springer, Cham. 2014. V. 8543. P. 169–183. URL: https://doi.org/10.1007/978-3-319-08434-3_13.</mixed-citation><mixed-citation xml:lang="en">Kohlhase M. A Data Model and Encoding for a Semantic, Multilingual Terminology of Mathematics // In: Watt S.M., et al. (Eds.) Proceedings of the International Conference on Intelligent Computer Mathematics (CICM 2014). Lecture Notes in Computer Science. . Springer, Cham. 2014. V. 8543. P. 169–183. URL: https://doi.org/10.1007/978-3-319-08434-3_13.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Nevzorova O., Zhiltsov N., Kirillovich A., Lipachev E. OntoMathPRO Ontology: A Linked Data Hub for Mathematics // In: Klinov P., Mouromstev D. (Eds.) Proc. of the 5th Int. Conf. on Knowledge Engineering and Semantic Web (KESW 2014). Communications in Computer and Information Science. Springer, Cham. 2014. V. 468. P. 105–119. https://doi.org/10.1007/978-3-319-11716-4_9.</mixed-citation><mixed-citation xml:lang="en">Nevzorova O., Zhiltsov N., Kirillovich A., Lipachev E. OntoMathPRO Ontology: A Linked Data Hub for Mathematics // In: Klinov P., Mouromstev D. (Eds.) Proc. of the 5th Int. Conf. on Knowledge Engineering and Semantic Web (KESW 2014). Communications in Computer and Information Science. Springer, Cham. 2014. V. 468. P. 105–119. https://doi.org/10.1007/978-3-319-11716-4_9.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Кириллович А.В., Жильцов Н.Г., Иваньшин П.Н., Каюмова А.В., Каюмов И.Р., Липачев Е.К., Матвейчук М.С., Невзорова О.А., Соловьев В.Д., Уткина Е.А. Онтология профессиональной математики «OntoMathPRO» // Свидетельство о регистрации базы данных RU 2018622131, 25.12.2018.</mixed-citation><mixed-citation xml:lang="en">Кириллович А.В., Жильцов Н.Г., Иваньшин П.Н., Каюмова А.В., Каюмов И.Р., Липачев Е.К., Матвейчук М.С., Невзорова О.А., Соловьев В.Д., Уткина Е.А. Онтология профессиональной математики «OntoMathPRO» // Свидетельство о регистрации базы данных RU 2018622131, 25.12.2018.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Ginev D., Iancu M., Jucovshi C., Kohlhase A., Kohlhase M., Oripov A., Schefter J., Sperber W., Teschke O., and Wiesing T. The SMGloM Project and System: Towards a Terminology and Ontology for Mathematics // In: Greuel G.M. et al. (Eds.) 5th International Conference on Mathematical Software (ICMS 2016). Lecture Notes in Computer Science. Springer, Cham. 2016. V. 9725. P. 451–457. https://doi.org/10.1007/978-3-319-42432-3_58.</mixed-citation><mixed-citation xml:lang="en">Ginev D., Iancu M., Jucovshi C., Kohlhase A., Kohlhase M., Oripov A., Schefter J., Sperber W., Teschke O., and Wiesing T. The SMGloM Project and System: Towards a Terminology and Ontology for Mathematics // In: Greuel G.M. et al. (Eds.) 5th International Conference on Mathematical Software (ICMS 2016). Lecture Notes in Computer Science. Springer, Cham. 2016. V. 9725. P. 451–457. https://doi.org/10.1007/978-3-319-42432-3_58.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Tzoumpa D., Mitropoulos S. Semantic Web Technologies for Ontologies Description: Case study in Geometry Education // In: 2020 5th South-East Europe Design Automation, Computer Engineering, Computer Networks and Social Media Conference (SEEDA-CECNSM), Corfu, Greece. 2020. P. 1–5.</mixed-citation><mixed-citation xml:lang="en">Tzoumpa D., Mitropoulos S. Semantic Web Technologies for Ontologies Description: Case study in Geometry Education // In: 2020 5th South-East Europe Design Automation, Computer Engineering, Computer Networks and Social Media Conference (SEEDA-CECNSM), Corfu, Greece. 2020. P. 1–5.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">https://doi.org/10.1109/SEEDA-CECNSM49515.2020.9221781.</mixed-citation><mixed-citation xml:lang="en">https://doi.org/10.1109/SEEDA-CECNSM49515.2020.9221781.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Anderson J.Q. Individualisation of Higher Education: How Technological Evolution can Revolutionise Opportunities for teaching and learning // International social science journal. 2013. V. 64. No. 213–214. P.305–316.</mixed-citation><mixed-citation xml:lang="en">Anderson J.Q. Individualisation of Higher Education: How Technological Evolution can Revolutionise Opportunities for teaching and learning // International social science journal. 2013. V. 64. No. 213–214. P.305–316.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">https://doi.org/10.1111/issj.12046.</mixed-citation><mixed-citation xml:lang="en">https://doi.org/10.1111/issj.12046.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Абрамский М.М., Батырова Э.Ф., Марданова А.Р., Ахметзянова Т.А. Генерация индивидуальных образовательных траекторий и расписания обучения в парадигме индивидуализации образования // Электронные библиотеки. 2018. Т 21. № 3–4. С. 129–145.</mixed-citation><mixed-citation xml:lang="en">Абрамский М.М., Батырова Э.Ф., Марданова А.Р., Ахметзянова Т.А. Генерация индивидуальных образовательных траекторий и расписания обучения в парадигме индивидуализации образования // Электронные библиотеки. 2018. Т 21. № 3–4. С. 129–145.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Муромцев Д.И. Модели и методы индивидуализации электронного обучения в контексте онтологического подхода // Онтологии проектирования. 2020. Т. 10, № 1. С. 34–49. https://doi.org/10.18287/2223-9537-2020-10-1-34-49.</mixed-citation><mixed-citation xml:lang="en">Муромцев Д.И. Модели и методы индивидуализации электронного обучения в контексте онтологического подхода // Онтологии проектирования. 2020. Т. 10, № 1. С. 34–49. https://doi.org/10.18287/2223-9537-2020-10-1-34-49.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Галеев Р.Д., Гильманшин И.Р., Кашапов Н.Ф., Гильманшина С.И. Применение индивидуальных образовательных траекторий и адаптивного контента в инженерном образовании // Перспективы и приоритеты педагогического образования в эпоху трансформаций, выбора и вызовов. сборник научных трудов VI Виртуального Международного форума по педагогическому образованию. Казань, 2020. С. 120–129.</mixed-citation><mixed-citation xml:lang="en">Галеев Р.Д., Гильманшин И.Р., Кашапов Н.Ф., Гильманшина С.И. Применение индивидуальных образовательных траекторий и адаптивного контента в инженерном образовании // Перспективы и приоритеты педагогического образования в эпоху трансформаций, выбора и вызовов. сборник научных трудов VI Виртуального Международного форума по педагогическому образованию. Казань, 2020. С. 120–129.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Абрамский М.М. Управление данными в современных цифровых образовательных средах // Информационное общество. 2019. № 1–2. С. 82–91.</mixed-citation><mixed-citation xml:lang="en">Абрамский М.М. Управление данными в современных цифровых образовательных средах // Информационное общество. 2019. № 1–2. С. 82–91.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Абрамский М.М. Модели, методы и программные средства управления данными цифровых образовательных сред. Дис.к.т.н…. Казань, 2019. 160 с.</mixed-citation><mixed-citation xml:lang="en">Абрамский М.М. Модели, методы и программные средства управления данными цифровых образовательных сред. Дис.к.т.н…. Казань, 2019. 160 с.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Kirillovich A., Nevzorova O., Falileeva M., Lipachev E., Shakirova L. OntoMathEdu:Towards an Educational Mathematical Ontology // In: Edwin B. et al. (Eds). Workshop Papers at 12th Conference on Intelligent Computer Mathematics (CICM-WS 2019), Prague, Czech Republic, 8–12 July 2019. CEUR Workshop Proceedings. 2020. V. 2634. http://ceur-ws.org/Vol-2634/WiP1.pdf, last accessed 2020/11/21.</mixed-citation><mixed-citation xml:lang="en">Kirillovich A., Nevzorova O., Falileeva M., Lipachev E., Shakirova L. OntoMathEdu:Towards an Educational Mathematical Ontology // In: Edwin B. et al. (Eds). Workshop Papers at 12th Conference on Intelligent Computer Mathematics (CICM-WS 2019), Prague, Czech Republic, 8–12 July 2019. CEUR Workshop Proceedings. 2020. V. 2634. http://ceur-ws.org/Vol-2634/WiP1.pdf, last accessed 2020/11/21.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Falileeva M., Kirillovich A., Shakirova L., Nevzorova O., Lipachev E., Dyupina A. OntoMathEdu Educational Mathematical Ontology: Prerequisites, Educational Levels and Educational Projections. // CEUR Workshop Proceedings. 2020. V. 2784. P. 346–351. http://ceur-ws.org/Vol-2784/.</mixed-citation><mixed-citation xml:lang="en">Falileeva M., Kirillovich A., Shakirova L., Nevzorova O., Lipachev E., Dyupina A. OntoMathEdu Educational Mathematical Ontology: Prerequisites, Educational Levels and Educational Projections. // CEUR Workshop Proceedings. 2020. V. 2784. P. 346–351. http://ceur-ws.org/Vol-2784/.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Loukachevitch N., Komissarov A., Dobrov B., Shternov S. Using Ontology for Natural Sciences and Technologies for Vacancies Analysis // DTTL-2021: International Workshop on Digital Technologies for Teaching and Learning, March 22-28, 2021, Kazan, Russia. 2021 (in press).</mixed-citation><mixed-citation xml:lang="en">Loukachevitch N., Komissarov A., Dobrov B., Shternov S. Using Ontology for Natural Sciences and Technologies for Vacancies Analysis // DTTL-2021: International Workshop on Digital Technologies for Teaching and Learning, March 22-28, 2021, Kazan, Russia. 2021 (in press).</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Kirillovich A., Nevzorova O., Falileeva M., Lipachev E., Shakirova L. OntoMathEdu: a New Linguistically Grounded Educational Mathematical Ontology // In: Benzmüller C. and Miller B. (Eds.) Proc. of the 13th International Conference on Intelligent Computer Mathematics (CICM 2020). Lecture Notes in Artificial Intelligence. Springer. 2020. V. 12236. P. 157–172.</mixed-citation><mixed-citation xml:lang="en">Kirillovich A., Nevzorova O., Falileeva M., Lipachev E., Shakirova L. OntoMathEdu: a New Linguistically Grounded Educational Mathematical Ontology // In: Benzmüller C. and Miller B. (Eds.) Proc. of the 13th International Conference on Intelligent Computer Mathematics (CICM 2020). Lecture Notes in Artificial Intelligence. Springer. 2020. V. 12236. P. 157–172.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Шакирова Л.Р., Фалилеева М.В., Кириллович А.В., Липачев Е.К. Проектирование образовательной математической онтологии: проблемы и методы решения на примере курса планиметрии // XV Международная конференция по компьютерной и когнитивной лингвистике TEL 2018. Сборник трудов: в 2-х томах. Т. 1. Казань: Изд.-во АН РТ. 2018. С. 393–405.</mixed-citation><mixed-citation xml:lang="en">Шакирова Л.Р., Фалилеева М.В., Кириллович А.В., Липачев Е.К. Проектирование образовательной математической онтологии: проблемы и методы решения на примере курса планиметрии // XV Международная конференция по компьютерной и когнитивной лингвистике TEL 2018. Сборник трудов: в 2-х томах. Т. 1. Казань: Изд.-во АН РТ. 2018. С. 393–405.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Кириллович А.В., Липачев Е.К., Невзорова О.А., Фалилеева М.В., Шакирова Л.Р. Онтология образовательной математики «OntoMathEDU» // Свидетельство о регистрации базы данных RU 2019622208, 28.11.2019.</mixed-citation><mixed-citation xml:lang="en">Кириллович А.В., Липачев Е.К., Невзорова О.А., Фалилеева М.В., Шакирова Л.Р. Онтология образовательной математики «OntoMathEDU» // Свидетельство о регистрации базы данных RU 2019622208, 28.11.2019.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Elizarov A.M., Lipachev E.K. Lobachevskii DML: Towards a Semantic Digital Mathematical Library of Kazan University // CEUR Workshop Proceedings. 2017. V. 2022. P. 326–333.</mixed-citation><mixed-citation xml:lang="en">Elizarov A.M., Lipachev E.K. Lobachevskii DML: Towards a Semantic Digital Mathematical Library of Kazan University // CEUR Workshop Proceedings. 2017. V. 2022. P. 326–333.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Елизаров А.М., Жильцов Н.Г., Кириллович А.В., Липачев Е.К., Невзорова О.А. Экосистема OntoMATH и проект Всемирной цифровой математической библиотеки // Труды международной конференции по компьютерной и когнитивной лингвистике. Сер. "Интеллект. Язык. Компьютер" 2016. С. 25–28.</mixed-citation><mixed-citation xml:lang="en">Елизаров А.М., Жильцов Н.Г., Кириллович А.В., Липачев Е.К., Невзорова О.А. Экосистема OntoMATH и проект Всемирной цифровой математической библиотеки // Труды международной конференции по компьютерной и когнитивной лингвистике. Сер. "Интеллект. Язык. Компьютер" 2016. С. 25–28.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Elizarov A.M., Kirilovich A.V., Lipachev E.K., Nevzorova O.A. Mathematical Knowledge Management: Ontological Models and Digital Technology // CEUR Workshop Proceedings. 2016. V. 1752. P. 44–50. URL: http://ceur-ws.org/Vol-1752/paper08.pdf.</mixed-citation><mixed-citation xml:lang="en">Elizarov A.M., Kirilovich A.V., Lipachev E.K., Nevzorova O.A. Mathematical Knowledge Management: Ontological Models and Digital Technology // CEUR Workshop Proceedings. 2016. V. 1752. P. 44–50. URL: http://ceur-ws.org/Vol-1752/paper08.pdf.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Elizarov A.M., Kirillovich A.V., Lipachev E.K., Zhizhchenko A.B., Zhil’tsov N.G. Mathematical Knowledge Ontologies and Recommender Systems for Collections of Documents in Physics and Mathematics // Doklady Mathematics. 2016. V. 93, No. 2. P. 231–233. https://doi.org/10.1134/S1064562416020174.</mixed-citation><mixed-citation xml:lang="en">Elizarov A.M., Kirillovich A.V., Lipachev E.K., Zhizhchenko A.B., Zhil’tsov N.G. Mathematical Knowledge Ontologies and Recommender Systems for Collections of Documents in Physics and Mathematics // Doklady Mathematics. 2016. V. 93, No. 2. P. 231–233. https://doi.org/10.1134/S1064562416020174.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Elizarov A., Kirillovich A., Lipachev E., Nevzorova O. Semantic Formula Search in Digital Mathematical Libraries // Proc. of the 2nd Russia and Pacific Conf. on Comp. Technology and Applications (RPC 2017). IEEE. 2017. P. 39–43. https://doi.org/10.1109/RPC.2017.8168063.</mixed-citation><mixed-citation xml:lang="en">Elizarov A., Kirillovich A., Lipachev E., Nevzorova O. Semantic Formula Search in Digital Mathematical Libraries // Proc. of the 2nd Russia and Pacific Conf. on Comp. Technology and Applications (RPC 2017). IEEE. 2017. P. 39–43. https://doi.org/10.1109/RPC.2017.8168063.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Falileeva M., Kirillovich A., Shakirova L., Nevzorova O., Lipachev E., Dyupina A. OntoMathEdu Educational Mathematical Ontology: Prerequisites, Educational Levels and Educational Projections. // CEUR Workshop Proceedings. 2020. V. 2784. P. 346–351. http://ceur-ws.org/Vol-2784/.</mixed-citation><mixed-citation xml:lang="en">Falileeva M., Kirillovich A., Shakirova L., Nevzorova O., Lipachev E., Dyupina A. OntoMathEdu Educational Mathematical Ontology: Prerequisites, Educational Levels and Educational Projections. // CEUR Workshop Proceedings. 2020. V. 2784. P. 346–351. http://ceur-ws.org/Vol-2784/.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Федеральные государственные образовательные стандарты. Основное общее образование (5–9 кл.). URL: https://fgos.ru/#b3ac23ba5e3cfc8ef, https://fgos.ru/LMS/wm/wm_fgos.php?id=osnov.</mixed-citation><mixed-citation xml:lang="en">Федеральные государственные образовательные стандарты. Основное общее образование (5–9 кл.). URL: https://fgos.ru/#b3ac23ba5e3cfc8ef, https://fgos.ru/LMS/wm/wm_fgos.php?id=osnov.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">The national curriculum. URL: https://www.gov.uk/national-curriculum.</mixed-citation><mixed-citation xml:lang="en">The national curriculum. URL: https://www.gov.uk/national-curriculum.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">National curriculum in England: mathematics programmes of study. URL: https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study/national-curriculum-in-england-mathematics-programmes-of-study.</mixed-citation><mixed-citation xml:lang="en">National curriculum in England: mathematics programmes of study. URL: https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study/national-curriculum-in-england-mathematics-programmes-of-study.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Standards for Mathematical Practice.</mixed-citation><mixed-citation xml:lang="en">Standards for Mathematical Practice.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">URL: http://www.corestandards.org/Math/Practice/.</mixed-citation><mixed-citation xml:lang="en">URL: http://www.corestandards.org/Math/Practice/.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Cummins J., Carter J.A., Cuevas G.J., Day R, Malloy C. Glencoe Geometry, Virginia Student Edition. McGraw-Hill/Glencoe, 2012. 810 p.</mixed-citation><mixed-citation xml:lang="en">Cummins J., Carter J.A., Cuevas G.J., Day R, Malloy C. Glencoe Geometry, Virginia Student Edition. McGraw-Hill/Glencoe, 2012. 810 p.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Gantert A.X. Amsco's Geometry. AMSCO School Publications, Incorporated, 2008. 643 p.</mixed-citation><mixed-citation xml:lang="en">Gantert A.X. Amsco's Geometry. AMSCO School Publications, Incorporated, 2008. 643 p.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Larson R.L., Boswell L., Stiff L. Heath Geometry an Integrared Approach. Teacher’s Edition, 1998. 876 p.</mixed-citation><mixed-citation xml:lang="en">Larson R.L., Boswell L., Stiff L. Heath Geometry an Integrared Approach. Teacher’s Edition, 1998. 876 p.</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">KS2 Maths SATs Study Book: For the 2021 Tests (Collins KS2 SATs Practice). Collins KS2, 2015. 112 p.</mixed-citation><mixed-citation xml:lang="en">KS2 Maths SATs Study Book: For the 2021 Tests (Collins KS2 SATs Practice). Collins KS2, 2015. 112 p.</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">KS3 Maths Complete Revision &amp; Practice - Higher (with Online Edition) (Paperback). CGP Books, 2014. 171 p.</mixed-citation><mixed-citation xml:lang="en">KS3 Maths Complete Revision &amp; Practice - Higher (with Online Edition) (Paperback). CGP Books, 2014. 171 p.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Joinson R. Exercises in KS3 Mathematics Levels 5-6 (Spiral bound). 2001. 101 p.</mixed-citation><mixed-citation xml:lang="en">Joinson R. Exercises in KS3 Mathematics Levels 5-6 (Spiral bound). 2001. 101 p.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">Pereira C.K., Matsui Siqueira S.W., Nunes B.P., Dietze S. Linked Data in Education: A Survey and a Synthesis of Actual Research and Future Challenges // IEEE Transactions on Learning Technologies. 2018. V. 11, No. 3. P. 400–412.</mixed-citation><mixed-citation xml:lang="en">Pereira C.K., Matsui Siqueira S.W., Nunes B.P., Dietze S. Linked Data in Education: A Survey and a Synthesis of Actual Research and Future Challenges // IEEE Transactions on Learning Technologies. 2018. V. 11, No. 3. P. 400–412.</mixed-citation></citation-alternatives></ref><ref id="cit41"><label>41</label><citation-alternatives><mixed-citation xml:lang="ru">https://doi.org/10.1109/TLT.2017.2787659.</mixed-citation><mixed-citation xml:lang="en">https://doi.org/10.1109/TLT.2017.2787659.</mixed-citation></citation-alternatives></ref><ref id="cit42"><label>42</label><citation-alternatives><mixed-citation xml:lang="ru">D’Aquin M. On the Use of Linked Open Data in Education: Current and Future Practices // In: Mouromtsev D. and D’Aquin M.(Eds.) Open Data for Education: Linked, Shared, and Reusable Data for Teaching and Learning. Lecture Notes in Computer Science, Springer, Cham. 2016. V. 9500. P. 3–15.</mixed-citation><mixed-citation xml:lang="en">D’Aquin M. On the Use of Linked Open Data in Education: Current and Future Practices // In: Mouromtsev D. and D’Aquin M.(Eds.) Open Data for Education: Linked, Shared, and Reusable Data for Teaching and Learning. Lecture Notes in Computer Science, Springer, Cham. 2016. V. 9500. P. 3–15.</mixed-citation></citation-alternatives></ref><ref id="cit43"><label>43</label><citation-alternatives><mixed-citation xml:lang="ru">https://doi.org/10.1007/978-3-319-30493-9_1.</mixed-citation><mixed-citation xml:lang="en">https://doi.org/10.1007/978-3-319-30493-9_1.</mixed-citation></citation-alternatives></ref><ref id="cit44"><label>44</label><citation-alternatives><mixed-citation xml:lang="ru">Borgo S., Masolo C. Ontological Foundations of DOLCE // In: Poli R., Healy M., Kameas A. (Eds.) Theory and Applications of Ontology. Computer Applications. Dordrecht: Springer, 2010. P. 279–295.</mixed-citation><mixed-citation xml:lang="en">Borgo S., Masolo C. Ontological Foundations of DOLCE // In: Poli R., Healy M., Kameas A. (Eds.) Theory and Applications of Ontology. Computer Applications. Dordrecht: Springer, 2010. P. 279–295.</mixed-citation></citation-alternatives></ref><ref id="cit45"><label>45</label><citation-alternatives><mixed-citation xml:lang="ru">Gangemi A., Mika P. Understanding the Semantic Web through Descriptions and Situations // In: Meersman R., Tari Z., Schmidt D.C. (Eds.) On The Move to Meaningful Internet Systems 2003: CoopIS, DOA, and ODBASE. OTM 2003. Lecture Notes in Computer Science, Berlin, Heidelberg: Springer. 2003. V. 2888. P. 689–706.</mixed-citation><mixed-citation xml:lang="en">Gangemi A., Mika P. Understanding the Semantic Web through Descriptions and Situations // In: Meersman R., Tari Z., Schmidt D.C. (Eds.) On The Move to Meaningful Internet Systems 2003: CoopIS, DOA, and ODBASE. OTM 2003. Lecture Notes in Computer Science, Berlin, Heidelberg: Springer. 2003. V. 2888. P. 689–706.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
